So I just checked again. 2 houses in the immediate vicinity (2-3 houses next door) actually have houses as rear development. I hope that this way I can argue with the BA
Look at the development plan that is relevant for you.
The blue lines mark the current building windows. As you can see, the actual development on some plots deviates from this, which indicates that the development is older than the development plan from 1968. The deviations can therefore very likely be explained by Grandfather protection, which can be seen, for example, on plots 679 and 680, which you are probably referring to, because border distances etc. are not observed there. Under today's planning law, you probably would no longer get approval there.
The same even applies to your plot – your house extends out of the building window to the north (which is somewhat odd, since according to your information the house was only built in 1972, i.e. 4 years after the development plan was established). If you were to demolish your house, you would not be allowed to rebuild it in the same place but would have to adhere to the building window in the standard case and move the house southwards.
Well, asking doesn't cost anything in the end, but I see better chances in bundling all owners together and making densification of developed areas appealing to the city planners.
When arguing, it doesn't hurt to think like a city planner: if they gave you a building permit that is only very, very slightly legally contestable, they would have the corresponding lawsuit on the table faster than you can spell your name. They have no interest in that – it only costs money, nerves, and brings in nothing.
Therefore, all neighbors/owners must first be convinced that this is a cool idea. If that is the case, the effort is worth it for the city – otherwise not.
Best regards Dirk Grafe